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Full text of "Analytical Mechanics"

56                         ANALYTICAL MKCHANK'S
6. Prove that the resisting torque due to Motion is ^ivat.r 1W a hollow pivot than for a solid pivot, provided thai tho load and ||H. Inad P,r unit, area are the same in both cases.                    _                             ,
7 Show that the resisting torque duo to trirtion tor a hi>misphi-n-:il pivot is about 2.35 times as large as tluit fur a flat end pivot.
ROLLING  KRUTIOX.
59. Coefficient of Rolling Friction.    -('ons'idcr :i cylinder, Fig. 40, which is in equilibrium on a rough horizontal plum* under the action of a force S-In addition to this force the cylinder is acted upon by its weight and by the reaction of the plane.   Applying the conditions of equilibrium we obtain
Y
where F and N are the components of R, the reaction of the plane, while D and d arc, respectively, the distances of the points of application of R and S from the point 0, about which the moments are taken. These equations give* us
Piti, 40.
(1)
and
D-'d.
If the cylinder is just on the point of motion
and consequently